As explained in  sec:intro, auto-regressive models like PixelCNN [1]} fail in decompression speed due to their dependencies nature because it is hard to parallelize the inference process.
Fortunately, our AR module could be parallelized during inference. fig:aeparallel suggests one step in decoding. For the red channel, the current point is dependent on its up, left, upper-left points, so anti-diagonal points can be calculated in parallel.
Once the red channel is recovered, for the green channel, we could calculate column by column to recover this channel, and the blue channel is the same.
Thus, more points could be calculated at one time, which speeds up the inference process of the AR module. Because the padding rule is fixed, we could eventually losslessly recover the original image \(x\)  using the residual \(r\) .
